报告题目：Gluing compactly generated t-structures over stalks of affine schemes

报告人：胡江胜 教授 杭州师范大学

邀请人：李欢欢

报告时间：2024年5月12日（周日）10：30

报告地点： 行政辅楼235会议室

报告人简介： 胡江胜，杭州师范大学教授。主要从事同调代数与代数表示理论等领域的研究，研究领域涉及逼近理论、高维同调理论、Gorenstein同调理论与复形的相对上同调理论等。在Israel J. Math.，Quart. J. Math.，J. Algebra，J. Pure Appl. Algebra，Sci. China Math. 等国内外著名数学期刊上发表学术论文40余篇；多次应邀在中日韩国际环论会议、全国代数学学术会议等国内外重要会议上作大会报告。主持国家自然科学基金面上项目、青年项目、数学天元基金项目等科研项目多项。

报告摘要：In this talk, we show that compactly generated t-structures in the derived category of a commutative ring R are in a bijection with certain families of compactly generated t-structures over the local rings Rm where m runs through the maximal ideals in the Zariski spectrum Spec(R). The families are precisely those satisfying a gluing condition for the associated sequence of Thomason subsets of Spec(R). As one application, we generalize the results of Trlifaj and Sahinkaya and establish an explicit bijection between cosilting objects of cofinite type over R and compatible families of cosilting objects of cofinite type over all localizations Rm at maximal primes. Furthermore, we show that the -Telescope Conjecture for a quasi-coherent and quasi-separated scheme is a stalk-local property. This talk is based on a joint work with Michal Hrbek and Rongmin Zhu.

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